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Triple Action Hold 'Em

Introduction

I noticed Triple Action Hold 'Em at Binion's Horseshoe on May 1, 2009. It is also offered at Internet casinos using Cryptologic software. It is a fairly simple poker based game, where you go against the dealer. What makes this game different from the recent batch of poker variants is this one is based on five cards, and uses only a 28-card deck.

Rules

A modified 28-card deck is used, consisting only of the eights to aces.

Play starts with three bets available to the player, the Ante, Flop Bet, and Bonus Bet.

The dealer will deal each player, and himself, two hole cards. In addition, there is one three-card flop, which is dealt face down. The players' hole cards are dealt face down, while the dealer's cards are dealt one up and one down.

The player must either make a Raise bet or fold. The Raise bet must be equal to the Ante bet. If the player folds, then he loses his Ante wager.

The dealer turns exposed his other hole card and the flop.

If the dealer's five-card poker hand is a pair of nines or greater, then he shall qualify.

If the dealer does not qualify, then the ante bet shall pay even money, and the raise shall push.

If the dealer does qualify, then the player's five-card poker hand will be compared to the dealer's; the higher hand wins. If the player has the higher hand, then the Ante and Raise shall pay even money. If the dealer has the higher hand, then the Ante and Raise shall lose. An exact tie results in a push.

If the player did not fold, and his hand is a full house or better, then he shall be paid an Ante Bonus, according to the pay table below, which is based on the amount of the Ante wager. It is not required to beat the dealer for purposes of the Ante Bonus.

Regardless of who wins between the player and dealer, the Flop and Bonus bets shall pay according to the pay tables below. I presume that if the player folds, he still can win the Bonus bet.

Ante Bonus Pay Table

Five-Card Hand

Pays

Royal flush

50 to 1

Straight flush

20 to 1

Flush

6 to 1

Four of a kind

4 to 1

Full house

2 to 1

All other

None

Flop Bet Pay Table

Five-Card Hand

Pays

Straight flush

10 to 1

Three of a kind

10 to 1

Flush

4 to 1

Straight

2 to 1

Jacks or better

1 to 1

All other

Loss

Bonus Bet Pay Table

Five-Card Hand

Pays

Royal flush

100 to 1

Straight flush

50 to 1

Flush

25 to 1

Four of a kind

15 to 1

Full house

8 to 1

Straight

6 to 1

Three of a kind

3 to 1

Two pair

1 to 1

All other

Loss

Strategy

The optimal strategy on the Ante bet is to always raise. Of the three bets, the element of risk is lowest on the Ante bet, at 1.82%. I often get asked about the optimal mixture of bets for games like this. In this case, it is 100% on the Ante, and 0% on the Flop and Bonus bets.

Ante Bet Analysis

The return table below shows the return before factoring in the Ante Bonus.

Ante Bet Analysis

Event

Pays

Combinations

Probability

Return

Win

2

68426184

0.275193

0.550385

Dealer doesn't qualify

1

65881200

0.264957

0.264957

Push

0

4053024

0.0163

0

Lose

-2

110287992

0.44355

-0.8871

Totals

248648400

1

-0.071758

The next table shows the contribution to the return of the Ante Bonus.

Ante Bonus Analysis

Event

Pays

Combinations

Probability

Return

Royal flush

50

4

0.000041

0.002035

Straight flush

20

8

0.000081

0.001628

Flush

6

72

0.000733

0.004396

Four of a kind

4

168

0.001709

0.006838

Full house

2

1008

0.010256

0.020513

All other

0

97020

0.987179

0

Total

98280

1

0.035409

The overall return on the Ante bet is -0.071758 + 0.035409 = -0.036349. So the house edge is 3.63%. The player should always raise, so the average final bet is two units, making the element of risk = 3.63%/2 = 1.82%.